Your last point is a none issue. What is clear from genesis is we are supposed to be able to distinguish between good and evil whether god is involved or not. Jesus commandments gave us a more precise set of rules but the core framework comes from what we are not the bible. We are in essence on this aspect now like God but unlike God we are also sinners and give in to temptation. This means that whilst morality will existe without God, it will have tendency of being misguided. So I have no problem with with what the AHA are doing, I just think its unlikely that morality without God would not lead to the morality we have today in the west which based on Christian morality but to one which is probably much less tolerant.
It also worth noting that Richard Dawkins is the poster child of new atheism. Whilst most wont make the distinction with atheism, their are many atheist that are highly critical of the new atheist movement in part because his arguments are getting seriously close to scientism. To an extent new atheism is to atheism what islamiste are to Muslims, or groups like Westboro Baptist Church are to Christians.
As for the “canceling”, I hate that buzz word. Its presented as an action of free speech, when in reality it a form of free speech that people claiming its not often use to chase people they don’t like away from their channels. Its also to defend something intent when that something never had that intent. Unless moderators green light me, I’m not going to give examples here as they could be contraversial and be political.
On the other hand, I don’t like removing peoples titles for unrelated topics, for example I feel the Henry Ford should be recognized as the man the popularized chain production even though he was an anti-semite and apparently quite a despicable man. But this case might be different. If the objective of the AHA is to prove modern morality through logic and science then yes Richard Dawkins actions kinda go in the opposite way. They go more in the direction I’d expect them to go without the guidance of God but that is irrelavent if that not what the AHA believe and stand for.